Theorem orbi12i

Description: Infer the disjunction of two equivalences. (Contributed by NM, 3-Jan-1993)

	Ref	Expression
Hypotheses	orbi12i.1	$$⊢\phi \leftrightarrow \psi$$
	orbi12i.2	$$⊢\chi \leftrightarrow \theta$$
Assertion	orbi12i	$$⊢\left(\phi \vee \chi \right)\leftrightarrow \left(\psi \vee \theta \right)$$

Proof

Step	Hyp	Ref	Expression
1		orbi12i.1	$$⊢\phi \leftrightarrow \psi$$
2		orbi12i.2	$$⊢\chi \leftrightarrow \theta$$
3	2	orbi2i	$$⊢\left(\phi \vee \chi \right)\leftrightarrow \left(\phi \vee \theta \right)$$
4	1	orbi1i	$$⊢\left(\phi \vee \theta \right)\leftrightarrow \left(\psi \vee \theta \right)$$
5	3 4	bitri	$$⊢\left(\phi \vee \chi \right)\leftrightarrow \left(\psi \vee \theta \right)$$